Spatial light modulators (SLM) are transducers that modulate incident light in a spatial pattern corresponding to an electrical or optical input. The incident light may be modulated in its phase, intensity, polarization, or direction, and the light modulation may be achieved by a variety of material exhibiting various electrooptic or magnetooptic effects and by materials that modulate light by surface deformation. SLM's have found numerous applications in the areas of optical information processing, projections displays, and electrostatic printing. See references cited in L. Hornbeck, 128.times.128 Deformable Mirror Device, 30 IEEE Tran. Elec. Dev. 539 (1983).
Heretofore, in this field, a number of methods have been applied to achieve more than two phase and/or amplitude states in binary light modulators. Virtually all of these have been applied to magnetooptic modulators which are inherently binary but some can be applied to other modulators that are simply run in a binary fashion. Flannery et al., "Transform-ratio Ternary Phase-amplitude Filter Formulation for Improved Correlation Discrimination", Applied Optics 27, 4079-4083 (1988) and Kast et al., "Implementation of Ternary Phase Amplitude Filters Using a Magnetooptic Spatial Light Modulator", Applied Optics 28, 1044-1046 (1989) have described methods of using a ternary state that can be accessed in a magnetooptic modulator. Magnetooptic devices operate by switching the direction of the magnetic domain in a transmissive garnet material The domain direction can have only two states which leads to the inherently binary nature of the device.
A major disadvantage of the binary holograms and filters is that the binary representation is identical for both a hologram (or filter) and its complex conjugate. This means that when a binary hologram is reconstructed, both the desired image and a spatially reversed copy of the image (flipped in both the horizontal and vertical directions) are produced. Since neither the image nor its conjugate are preferred in this reconstruction, the total energy in the output is divided equally between the images reducing the efficiency of the process. In addition, the two reconstructions will overlap each other spatially unless special techniques such as spatial carriers are employed to separate these two images. Spatial carrier modulation will further reduce the overall efficiency of the reconstruction process.
Dickey and Hansche, "Quad-phase Correlation Filter Implementations", Applied Optics 28, 4840-4844 (1989) have described a method of using a binary state magnetooptic device to achieve four phase levels for correlation filters. The method uses a detour phase approach by operating the device aligned slightly off axis. The tilt used to give this misalignment provides a .pi./2 phase difference between adjacent pixels in the modulator in the tilt direction. By setting the processing resolution such that the responses from adjacent pixels mix together to give the net response, four phase states are possible: (.+-.1.+-.j)/.sqroot.2, (i.e., .pi./4, 3.pi./4, 5.pi./4, and 7.pi./4 radians). The technique requires critical alignment tolerances.
In U.S. patent application Ser. No. 590,405 filed Sept. 28, 1990, now U.S. Pat. No. 5,148,157, Florence has shown that full complex light modulation is possible by mixing the response of two adjacent phase modulating elements with analog addressing. The separate addressing of the two modulating elements provides the two degrees of freedom required to independently set both amplitude and phase in the combined pixel response. Although this method is quite general and provides complete modulation range in both amplitude and phase, it requires analog addressing circuitry.